Use the intercepts to graph the equation. \( 6 x-4 y=24 \) Use the graphing tool to graph the line. Use the

1. **Find the x-intercept** Set \( y = 0 \) in the equation: \[ 6x - 4(0) = 24 \quad \Rightarrow \quad 6x = 24 \] Solve for \( x \): \[ x = \frac{24}{6} = 4 \] So, the x-intercept is \((4, 0)\). 2. **Find the y-intercept** Set \( x = 0 \) in the equation: \[ 6(0) - 4y = 24 \quad \Rightarrow \quad -4y = 24 \] Solve for \( y \): \[ y = \frac{24}{-4} = -6 \] So, the y-intercept is \((0, -6)\). 3. **Graphing the Line** - Plot the intercepts \((4, 0)\) and \((0, -6)\) on the coordinate plane. - Draw a straight line through the points. This is the graph of the equation \[ 6x - 4y = 24. \] 4. **Alternative: Slope-Intercept Form** For further confirmation, rewrite the equation in the slope-intercept form: \[ 6x - 4y = 24 \quad \Rightarrow \quad -4y = 24 - 6x \] Divide both sides by \(-4\): \[ y = \frac{6x - 24}{4} = \frac{3}{2}x - 6 \] This confirms that the y-intercept is \((0, -6)\) and the slope is \(\frac{3}{2}\). Use the graphing tool to plot these points and draw the straight line through \((4, 0)\) and \((0, -6)\).